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Eilon Sharon, David van Dijk, Yael Kalma, et al. thousands of designed sequencesProbing the effect of promoters on noise in gene expression using

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Title: Probing the effect of promoters on noise in gene expression using thousands of designed sequences

Authors: Eilon Sharon1,2,3,†, David van Dijk1,2,†, Yael Kalma2, Leeat Keren1,2,

Ohad Manor1, Zohar Yakhini4,5 and Eran Segal1,2,* Affiliations: 1 Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel. 2 Department of Molecular Cell Biology, Weizmann Institute of Science, Rehovot, Israel. 3 Current address: Department of Genetics, Stanford University, Stanford, California 94305, USA 4 Computer Science Department, Technion, Haifa, Israel. 5 Agilent Laboratories, Santa Clara, California, USA. † These authors contributed equally to this work. * Correspondence to: E.Segal ([email protected]) Abstract: Genetically identical cells exhibit large variability (noise) in gene expression,

with important consequences for cellular function. Although the amount of noise

decreases with and is thus partly determined by the mean expression level, the extent

to which different promoter sequences can deviate away from this trend is not fully

known. Here, we present a high-throughput method for measuring promoter driven

noise for thousands of designed synthetic promoters in parallel. We use it to investigate

how promoters encode different noise levels and find that the noise levels of promoters

with similar mean expression levels can vary more than one order of magnitude, with

nucleosome-disfavoring sequences resulting in lower noise and more transcription

factor binding sites resulting in higher noise. We propose a kinetic model of gene

expression that takes into account the non-specific DNA binding and one-dimensional

sliding along the DNA, which occurs when transcription factors search for their target

sites. We show that this assumption can improve the prediction of the mean-

independent component of expression noise for our designed promoter sequences,

suggesting that transcription factor target search may affect gene expression noise.

Consistent with our findings in designed promoters, we find that binding site multiplicity

in native promoters is associated with higher expression noise. Overall, our results

Cold Spring Harbor Laboratory Press on November 7, 2014 - Published by genome.cshlp.orgDownloaded from



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demonstrate that small changes in promoter DNA sequence can tune noise levels in a

manner that is predictable and partly decoupled from effects on the mean expression

levels. These insights may assist in designing promoters with desired noise levels.

Main text:

Introduction

Stochastic cell-to-cell variability in gene expression (noise) can lead to substantial

phenotypic differences within a genetically identical cell population grown in the same

environment(Blake et al. 2003; Munsky et al. 2012). Therefore, maintaining low or high

noise levels for specific genes may provide an evolutionary advantage(Rainey et al.

2011; Acar et al. 2008; Beaumont et al. 2009). Indeed, genome-wide measurements of

protein levels reveal that genes exhibit different levels of stochastic noise(Bar-Even et al.

2006; Newman et al. 2006). These measurements display the qualitative trend that is

expected from a Poisson process of protein production and degradation(Bar-Even et al.

2006; Newman et al. 2006; Blake et al. 2003) in which noise decreases as mean

expression increases(Bar-Even et al. 2006; Newman et al. 2006). However, the

measured relationship between noise and mean expression does not quantitatively

match a Poisson process(Bar-Even et al. 2006; Newman et al. 2006; Blake et al. 2003),

and the results fit better to a model in which genes are transcribed in bursts that partly

result from promoters switching between active and inactive transcriptional states(Raser

and O’Shea 2004)(Paulsson 2004; So et al. 2011; Friedman et al. 2006). In this model

noise is affected by both the rate of transcriptional activation and the size of the

transcriptional bursts (the number of mRNA molecules produced at each instance of

promoter activation) (Sherman and Cohen 2014), and the number of proteins produced

by each mRNA. Therefore, according to this model, promoters can encode different

combinations of expression mean and noise, by modulating transcriptional bursting, as

shown experimentally in several studies(Amit et al. 2011; Dadiani et al. 2013; Hornung

et al. 2012; Raveh-Sadka et al. 2012; Choi and Kim 2009; Ozbudak et al. 2002).

However, we have a poor understanding of the extent to which promoters regulate




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noise beyond the level that is dictated by the mean and the sequence features by which

such regulation is encoded.

Genome-wide measurements of protein levels(Newman et al. 2006; Stewart-Ornstein et

al. 2012) do not isolate the effect of the promoter, since they represent the combined

effect of all layers of regulation. In addition, the local chromatin structure of the gene

may also affect its level of expression noise (Batenchuk et al. 2011). One way to isolate

this effect is to integrate the tested promoter upstream of a reporter gene and within a

fixed genomic context. Moreover, since the sequence of native promoters differs by

many parameters, mutated versions of native promoters(Hornung et al. 2012), synthetic

promoters built by random ligation of several building blocks(Mogno et al. 2010) or

designed synthetic promoters(Amit et al. 2011; Dadiani et al. 2013; Carey et al. 2013;

Murphy et al. 2007; Raveh-Sadka et al. 2012) are more suitable for studying the rules

by which promoter sequence affects noise. Previous such studies show that

nucleosome disfavoring sequences increase expression and reduce noise(Raveh-

Sadka et al. 2012; Dadiani et al. 2013; Choi and Kim 2009), whereas an equivalent

increase in mean expression that results from the addition of an activator binding site

increases noise(Dadiani et al. 2013) and that TATA boxes have little effect on

noise(Mogno et al. 2010). However, due to the difficulties of constructing synthetic

promoters, these studies were done on at most dozens of promoters. Thus, since no

effective high-throughput method of measuring promoter driven noise exists, the effect

on noise of much of the possible combinatorial complexity of promoter architecture has

not been tested to date.

Here, we study the effect of promoter sequence on noise in gene expression using

noise measurements of thousands of fully designed synthetic promoters with systematic

changes to the number, location and spacing of several regulatory elements. For this

aim, we devised a novel high-throughput method which is an extension of our previously

developed method(Sharon et al. 2012) that enables to obtain these thousands of

different noise measurements in a single experiment with a high agreement to

measurements of isolated strains (Pearson’s R2=0.80) and high reproducibility




4

(Pearson’s R2=0.78). Notably, we found that promoters with similar mean expression

levels in this set can vary by over more than one order of magnitude in their noise levels,

and that this large variation is similar to the variation found in native promoters(Bar-

Even et al. 2006; Carey et al. 2013). By examining the effect of various promoter

sequence elements on expression we find that nucleosome disfavoring sequences in

the promoter increase expression and decrease noise in a manner that correlates with

their length, consistent with observations on small sets of promoters(Raveh-Sadka et al.

2012). In addition, we find that larger and more dense clusters of transcriptional

activator binding sites yield noisier expression for a given mean expression level. We

show that a simple linear model can predict a large part of the variation in noise that is

independent of the mean expression, and that fitting two alternative kinetic models to

the data which assume different transcription factor DNA binding schemes, suggests

that non-specific DNA binding and one-dimensional sliding along the DNA of

transcription factors may play a role in how promoter sequence affects noise(Li et al.

2009; Hammar et al. 2012). Finally, we show that in native genes binding site multiplicity

is associated with higher noise.

Our work presents the largest measurement to date of promoter driven noise and an

investigation of how small and systematic changes in the promoter sequence affect

single-cell expression. The insights afforded by our work may provide the ability to tune

noise with little effect on mean expression and enhance our understanding of how

native promoters encode their noise levels. In addition, the method presented in this

work, which achieves at least an order of magnitude more data points than previous

studies, is scalable to other systems and organisms, and should be a useful tool for

studying DNA encoded single-cell gene expression in various systems.

Results Measuring the noise of thousands of designed promoters

To study the rules by which promoter sequences determine noise, we used a set of

6500 designed synthetic promoters with systematic manipulations to the affinity,

location, spacing, and number of several different regulatory elements. By devising new

analyses methods for an experimental approach that we previously developed(Sharon




5

et al. 2012), we extracted accurate noise measurements for each of these promoters.

Briefly, a pool of cells containing all 6500 promoters (one promoter per cell with each

promoter integrated upstream of a yellow fluorescent protein (YFP)) are first sorted by

their YFP expression level into 32 expression bins using fluorescence-activated cell

sorting (FACS). Next, the promoters of every expression bin are amplified and

sequenced using parallel sequencing. By counting the number of sequencing reads

obtained for each strain in every expression bin, we reconstruct the single cell

expression distribution of each promoter and from it, extract both its mean expression

and noise (Fig 1A-C; see Methods). We found that our method is highly reproducible

across replicates in terms of mean expression (Pearson’s R2=0.99, Fig. S1C), noise

(Pearson’s R2=0.78, Fig. S1A, measured as the variance divided by the mean squared,

also termed the squared Coefficient of Variation – CV2), and noise strength (Pearson’s

R2=0.75, Fig. S1B, measured as the variance divided by the mean, also termed the

Fano factor). More importantly, our measurements are highly accurate compared to

measurements of 54 isolated strains for mean (Pearson’s R2=0.97, Fig. S1F), noise

(Pearson’s R2=0.80, Fig. S1D), and noise strength (Pearson’s R2=0.88, Fig. S1E). Thus,

these results show that our approach can measure the noise of thousands of fully

designed promoters with an accuracy that approaches that obtained when constructing

and measuring each strain individually.

Examining the range of values spanned by our library, we found that the dynamic range

of both the mean expression and the noise of our synthetic promoters are similar to that

of native promoters, suggesting that our library is highly relevant for native

transcriptional regulation (Fig. S2). Notably, the noise levels of our synthetic promoters

span more than one order of magnitude even at similar mean expression levels (Fig. 1C). Since we designed the library such that many promoters differ by a small number

of base pair changes (e.g., changes to a single TFBS location or affinity), these results

demonstrate that even small base pair changes may result in large effects on noise.

Promoter sequence features determine the relation between expression mean and noise




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To study the rules by which promoter sequence determines gene expression noise, we

examined the effect on noise of systematic changes to the number and length of

poly(dT:dA) nucleosome disfavoring elements and to the number, location, and spacing

of transcription factor binding sites (TFBS). For poly(dT:dA) tracts, we compared the

expression of 1268 pairs of promoters that each differ by only a single insertion of a

15bp tract, and found that addition of such tracts results in a significant increase in the

mean expression (Fig. S3A, Student’s t-test P<10-170, Fig. S3D median increase of 86%

with 95% confidence intervals (CI): 76-93%) and a significant decrease in the noise (Fig. S3B, Student’s t-test P<10-26, Fig. S3D median decrease of 60% with 95% CI: 57-63%)

but has a significant though relatively smaller effect on the noise strength (Fig. S3C, Student’s t-test P<10-3, Fig. S3D median decrease of 12% with 95% CI: 7-16%).

Consistent with this effect of poly(dT:dA) tracts, we also found that longer tracts and,

separately, more tracts, increase mean expression, decrease noise, and have little

effect on noise strength (Fig. 2A, S4, S5). Assuming the promoter ON-OFF switching

model(Raser and O’Shea 2004), these results are qualitatively in line with poly(dT:dA)

tracts increasing expression mainly through an increase in the promoter on-switching

rate (burst frequency) rather than through an increase in promoter transcription rate

(which is linearly correlated with burst size) (see Supplementary Material for an

investigation of this model).

Next, we compared the effect on noise of increasing the mean expression by adding an

activator binding site versus adding a poly(dT:dA) tract, since a recent study that we

performed on a few strains showed that these two different strategies for increasing the

mean expression have opposing effects on noise. Notably, in 309 of 417 (74%)

promoters from our library for which adding a poly(dT:dA) tract resulted in a similar

increase in mean expression as did addition of an activator binding site, adding a

poly(dT:dA) tract resulted in significantly lower noise (Fig. 2B, binomial test P<10-22, Fig. S6). These results thus considerably expand the scope of our previous

observations(Dadiani et al. 2013) and suggest that nucleosome-disfavoring sequences

are an efficient tool for increasing expression while maintaining low noise.




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To examine the effect of varying the number and configuration of transcription activator

binding sites on noise, we examined a set of 643 promoters that contain 0-7 Gcn4

binding sites in various positions and background sequences. Notably, we found that for

a given expression level, promoters that contain more Gcn4 binding sites are noisier

(Fig. 2C, S7, ANOVA test P<10-19). This result also holds in a set of 443 promoters with

up to two binding sites for the transcription activator Leu3 (Fig. S8). These results thus

suggest that increasing the number of binding sites of transcription activating factors will

result in noisier expression.

To quantify the effect of promoter sequence features on the mean-independent

component of noise, we constructed a linear model that predicts mean expression from

promoter sequence features, and noise from either mean expression or from both mean

expression and promoter sequence features. We applied this model to two sets of

promoters, one consisting of 457 promoters with a single Gcn4 binding site in various

configurations and another consisting of 128 promoters with multiple Gcn4 binding sites

(all combinations of placing 0-7 Gcn4 binding sites in seven predefined positions). We

evaluated the performance of our model using a 5-fold cross-validation, in which we

split the data into 5 subsets and predicted the expression of each promoter using a

model that was trained on the 4 subsets that did not include the predicted promoter (Fig. 3, S9, S10). Notably, we found that although mean expression alone explains nearly

two-thirds (Pearson’s R2=0.63, Spearman’s ρ=0.74) and one-third (Pearson’s R2=0.33,

Spearman’s ρ=0.68) of the noise in both promoter sets (Fig. 3A,D), more than half of

the remaining noise can be explained by adding only a few sequence features to the

model (Pearson’s R2=0.82; Spearman’s ρ=0.89, Pearson’s R2=0.77; Spearman’s

ρ=0.88 respectively, Fig. 3B-C, 3E-F). Examining the set of features used by the model

(via their respective standardized weights, see Methods for details), we found that TFBS

affinity and multiplicity are the strongest predictors of the mean-independent component

of noise (Fig. 3C,F). We note that the latter might be expected, as it is the major

parameter changing between promoters. Since part of the variation in our data is due to

experimental error (Fig. S1), the above values are likely an underestimation. Overall,

these results demonstrate that a simple combination of changes to properties of




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nucleosome disfavoring elements and TF binding sites can account for much of the

effect of promoter sequence on the mean-independent component of noise.

A kinetic model of transcription factor target search can partly explain the mean-independent expression noise To obtain insights into the mechanism by which noise increases with TFBS number, we

explored the possibility that this effect partly results from the way in which TFs search

for their target sites. Transcription factors are known to search for their sites through

some combination of non-specific DNA binding via three-dimensional diffusion and

subsequent sliding across the DNA via one-dimensional diffusion(Hammar et al. 2012;

Khazanov et al. 2013). However, the extent to which these mechanisms affect

transcriptional regulation is not well understood. A recent study(Hammar et al. 2012)

showed that adjacent TFBS result in slower binding rates to each site, likely because a

TF molecule bound to one of the sites may limit the size of the region in which a second

TF molecule can slide in search of its target. Based on this observation, we

hypothesized that if 1D-sliding is indeed a major determinant of TF binding rate, then

promoters with multiple sites may have relatively slower TF binding kinetics and

therefore slower switching rates between transcriptionally active and inactive states,

possibly resulting in noisier expression.

To examine this hypothesis, we modeled a set of promoters with multiple Gcn4 binding

sites (all 128 combinations of 0-7 sites at seven predefined positions in two different

sequence contexts which differ by their GC content) using two models that differ in their

assumptions about how TFs search for their target sites. The first model (denoted 3D

model) assumes that TFs search their sites using only 3D-diffusion whereas the second

(denoted 3D+1D model) assumes a combination of 3D-diffusion and 1D-sliding.

Therefore in the second model the presence of a binding site can affect TF binding to a

neighboring site while in the first model the TF binds directly to each site independently

of other neighboring sites. The parameters of both models were the same except for an

additional TF sliding distance parameter in the 3D+1D model (see Methods for details).

For both models, we predict mean expression and noise by mapping each binding site




9

configuration to a unique kinetic scheme that is simulated or solved analytically (Fig. 4A,

see Methods). We used a 5-fold cross-validation scheme to compare the ability of the

two models to predict the expression mean and noise (Fig. 4B-C). We estimated their

performance both using the coefficient of determination (R2) and the Spearman’s rank

correlation coefficient (ρ) of the predictions to the measurements. We found that the

performance of the 3D+1D model on expression mean (R23D+1D=0.80±0.05,

ρ3D+1D=0.86±0.08) and expression noise (R23D+1D=0.51±0.15, ρ3D+1D=0.77±0.9) is

significantly better than the performance of the 3D model on expression mean

(R23D=0.68±0.09, ρ3D=0.83±0.05) and expression noise (R2

3D=0.17±0.2, ρ3D=0.57±1.3)

as shown by a Wilcoxon rank sum test on the distributions of R2 values for mean (P<10-

7) and noise (P<10-6), and on the distributions of Spearman’s correlation (ρ) values for

mean (P<0.05) and noise (P<10-6). Although additional mechanisms such as

cooperative binding(Giniger and Ptashne 1988; Miller and Widom 2003) and allosteric

effects(Kim et al. 2013; Amit et al. 2011) likely have effects, these results suggest TF

1D-sliding along the DNA as another mechanism which may affect gene expression

noise and could explain the observation that more TF binding sites result in higher noise

for the same mean expression level. Consistent with this idea, we found that native

promoters(Stewart-Ornstein et al. 2012) with higher affinity to TFs (Basehoar et al.

2004; MacIsaac et al. 2006; Portales-Casamar et al. 2010; Pachkov et al. 2013) or with

higher levels of TF binding(Venters et al. 2011) drive noisier gene expression (Fig. S13).

Discussion In summary, we presented the first large-scale investigation of fully designed systematic

changes to promoter sequence features on single-cell gene expression. For this aim we

developed a high-throughput approach that produces highly accurate and reproducible

noise measurements for thousands of fully designed sequences, in a single experiment.

We found that the noise of promoters with similar mean expression can vary more than

one order of magnitude, indicating that promoter sequence has a major effect on noise

beyond that which is mediated by the promoter’s mean expression level. Specifically,

we found that nucleosome-disfavoring sequences increase expression and reduce




10

noise, and that promoters with more transcriptional activator binding sites exhibit higher

noise. A linear model based on a small number of simple sequence features, in a

controlled setting, can predict much of the mean-independent effect of promoter

sequence on noise. We note that although our model explains our synthetic designed

promoters further development is required in order to apply similar models in more

general settings, i.e. on native promoter sequences. Finally, we fit to our measurements

two kinetic models of gene expression – one that assumes only TF three-dimensional

diffusion and a second model that assumes also TF one-dimensional sliding along the

DNA. The latter is able to better explain our measurements, and therefore suggests that

changes in binding kinetics, when sites are clustered and due to one-dimensional

sliding of TFs along the DNA, may have an affect on expression noise.

We note that in our experimental system the sole difference between the strains is their

promoter DNA sequence. Therefore, we assume that the differences in mean

expression and noise that we measured are a result of changes to the binding kinetics

of the transcriptional machinery, in turn affecting the size and the frequency of

transcriptional bursts. In other words, we assume that expression mean and noise

changes reflect changes in transcriptional bursting mediated by promoter DNA

sequence changes. While we and others(Zenklusen et al. 2008; Blake et al. 2006;

Carey et al. 2013; Dadiani et al. 2013; Hornung et al. 2012; Weinberger et al. 2005; Raj

et al. 2006) have previously found convincing evidence for the validity of this

assumption, further work is necessary to prove if and to what extent transcriptional

bursting can have effects on noise at the protein level, since this assumption was only

proven for protein bursting (Friedman et al. 2006).

In line with the above interpretation of the results and assuming a promoter ON-OFF

switching model(Raser and O’Shea 2004), our finding that nucleosome-disfavoring

sequences increase expression and reduce noise with significant though much smaller

effect on noise strength suggests that these elements may increase expression mainly

by increasing the promoter activation frequency (promoter ON switching rate), perhaps

by increasing the promoter’s accessibility to transcriptional activators. This result is




11

consistent with previous findings observed with a small set of promoters (Raveh-Sadka

et al. 2012; Dadiani et al. 2013).

We also found that other sequence features such as the affinity, number and

configuration of binding sites affect the mean-independent component of the noise, and

that a model based solely on DNA sequence features can predict a large part of the

expression mean and noise. This modeling task benefits from the controlled setting of

our synthetic promoter library, and although it is beyond the scope of this work, applying

such models to native promoters can improve our understanding of transcriptional

regulation in native settings.

Another notable finding is that the number and relative spacing of TF binding sites may

have large effects on noise. We observed that promoters with larger and denser

clusters of sites give higher noise level for a given mean expression both in our

designed promoters. Although, such direct observation on native promoters is still hard

due to their higher complexity, we did found evidence for this behavior also in native

promoters (Fig. S13). In search of a mechanism that can explain this observation, we

suggested a novel model of expression regulation which integrates TFs searching for

their targets using a combination of 3D-diffusion and 1D sliding(Hammar et al. 2012)

into the common model of transcription regulation that considers only 3D diffusion of

TFs(Gertz et al. 2009). We fitted these kinetic models to expression measurements of

promoters with all combinations of 7 predefined binding sites in two sequence contexts

and found that including 1D sliding significantly improves predicting the expression

mean and noise. Therefore, we suggest that slower TF binding kinetics, due to

decreased 1D-sliding of TFs, may in part explain how the number and configuration of

binding sites can affect promoter noise levels. Although it is known that TFs find their

targets by a combination of 3D-diffusion and 1D-sliding along the DNA, the relative

contribution of each of these mechanisms to the resulting expression behavior is not

well understood. Since homotypic TFBS clustering is a general organization principle of

cis-regulatory regions, as suggested by enrichment of such clusters in proximal

promoters and distal enhancers and by their conservation between vertebrate and




12

invertebrates(Wunderlich and Mirny 2009; Gotea et al. 2010; Weingarten-Gabbay and

Segal 2014), it is important to understand their effect on dynamics of transcription. Our

results, combined with our findings in native genes, suggest that competitive binding, as

a result of densely clustered binding sites, may be a mechanism that affects the

expression noise of native promoters. Since native promoters alone are possibly too

diverse to perform a structural investigation on, it will be interesting to conduct a similar

study on a library of native and mutated promoters. While our kinetic modeling scheme

is limited in several aspects, as it ignores chromatin effects and other more complex

models of transcription initiation, and assumes that transcriptional bursting is in part

controlled by DNA sequence and has significant effect on the noise, its ability to fit (in

cross-validation) both mean expression and noise better than a model that ignores one-

dimensional sliding may suggest that TF 1D-diffusion behavior has some non-negligible

consequences for transcriptional noise, and may be considered in any future models of

transcriptional regulation. In other words, although further study is needed to prove the

underling mechanisms, our work can stimulate further research in this direction. Our

results may also have implications for the understanding of the selective pressure

shaping promoter sequences as the organism may benefit from maintaining either low

or high noise for specific genes. Evidence of such selection is present in the finding that

yeast stress genes are noisier(Newman et al. 2006; Bar-Even et al. 2006).

Our approach has several limitations. First, the quality of our pooled noise

measurements is not as accurate as measuring isolated strains. Second, although we

analyze a relatively uniform cell population and normalize by our fixed promoter

regulated mCherry (red fluorescence) level, our results may include a pathway specific

extrinsic noise component. However, previous work in our lab showed that the level of

such noise is low (less than the lowest observed noise level)(Carey et al. 2013), and

that it accurately agrees with a dual reporter assay that only measures intrinsic

noise(Elowitz et al. 2002). Third, we assume that changes in transcriptional bursting can

be observed from changes in the protein level noise (i.e. higher noise is bigger bursts).

While this has been suggested in several studies (Cai et al. 2006; Friedman et al. 2006;

Elowitz et al. 2002; Hornung et al. 2012; Pedraza and Paulsson 2008) and previous




13

work in our lab showed convincing evidence that transcriptional bursting as measured

by time-lapse microscopy(Dadiani et al. 2013), can, at least in part, be controlled by

promoter sequence, much understanding is still lacking on the validity and significance

of this mechanism. We note that our measured protein abundance distributions reflect

bursts of both transcription and translation (from the produced mRNAs following the

activation of the promoter). Fourth, current data processing filters out promoters deriving

multimodal expression distribution. Since non of the isolated strains showed multimodal

distributions and almost all of our promoter have at least 75% of their reads within a

single distribution peak we do not expect that this filter removed considerable number of

promoters that derive true multimodal expression distribution; however removing this

filter is advised if the tested promoters may produce such distributions. Fifth, since in

our method the promoters are integrated into plasmids in a fixed position, we do not

measure the effect of the local chromatin structure on the promoter function (Batenchuk

et al. 2011). It would be interesting to investigate this effect by measuring the function of

our set of promoters in various genomic contexts. Finally, we note that since the core

promoter employed by our library is fixed and contains a TATA box, our results are

limited to TATA containing core promoters. Since TATA containing promoters are

associated with higher noise(Lehner 2010; Tirosh and Barkai 2008; Choi and Kim 2009),

it will be interesting to examine synthetic promoters in the context of TATA-less

promoters. In spite of these limitations, our ability to measure noise of thousands of

sequences within a single experiment paves the way for examining the effect on noise

of other promoter sequence features and of other regulatory layers such as post-

transcriptional and translational regulation.

Taken together, we presented a method for measuring designed promoter driven noise

in high-throughput and found that promoter sequence has profound effects on gene

expression noise, and that much of these effects are independent of the effect mediated

by the mean expression level. Aside from the biological insights that our results provide

on the extent to which different types of DNA sequence elements affect cell-to-cell

expression variability, our experimental framework offers powerful means by which

further research in this field may be carried out.




14

Methods Promoter library design construction and measurements

The promoter library was designed, constructed and measured as described in Sharon

et al.(Sharon et al. 2012), except for the differences below. Briefly, a large collection of

synthetic promoter reporter gene strains was generated by a pooled ligation of 6500

fully designed DNA oligos (obtained by synthesis on a microarray(LeProust et al. 2010)

by Agilent Technologies, Santa Clara, California). The oligos were ligated upstream to a

yellow fluorescent protein (YFP) gene with a short (100 bp) core promoter sequence

taken from HIS3 gene promoter and into a low copy plasmid that also contains a TEF2

promoter deriving red fluorescent protein (mCherry). The resulting plasmids were then

transformation into yeast (S. cerevisiae, strains: Y8205). Next, the pool of cells was

grown in amino acid starvation condition (SCD without amino acid except Histidine), and

sorted according to their YFP expression level into 32 expression bins (mCherry was

used for gating one plasmid copy cells and for normalization). The DNA of the

promoters in each bin were then amplified and sent to multiplexed parallel sequencing.

Each sequencing result was mapped to a specific promoter and expression bin,

resulting in a distribution of cells that contain each promoter across all expression bins.

The following differences were applied relative to the description in Sharon et.

al.(Sharon et al. 2012). The medium used both for growing the cells and for their sorting

was SC-Glu-URA (synthetic complete media with 2% glucose and without uracil)

medium without amino acids, except for Histidine. In order to achieve expression

distributions with high resolution that would allow good assessment of expression noise,

the library cells were sorted into 32 bins according to their ratio of YFP and mCherry

expression level, thereby normalizing for extrinsic noise effects. Each of the two

extreme expression bins contained 2% of the library cells and each of the remaining 30

bins contained 3.2%. We collected a total of 10,000,000 cells. As previously described,

the mapping of cells to bins involves parallel sequencing of the amplified promoter

regions. For this purpose, Illumina HiSeq 2000 was used to obtain >30,000,000 mapped

reads. The two replicates were separately generated from the ssDNA oligo library and

separately measured as described above.




15

High-throughput measurement of expression mean and variance For each promoter, the fraction of cells with that promoter in each expression bin was

estimated as described in Sharon et. al.(Sharon et al. 2012). Several new computational

procedures were then applied to filter and improve the accuracy of the results (see also

Supplementary Material). First, strains that were represented by less than 1000

sequencing reads (20% of the library) were filtered. Second, the distribution of each

strain across the expression bins was examined and the peak that contained the largest

fraction of cells of each strain was detected. The small fraction of cells outside of the

main peak was considered as technical noise and therefore set to zero. Note that this

assumes that the distribution is not multimodal, which holds for all of the isolated strains

and therefore most likely for the entire library. 2.2% of the strains for which the largest

peak contained less than 75% of the cells were filtered out (Fig. S13A). Third, to further

reduce the technical noise, a Gamma distribution was fitted to the cells distribution

across the bins (using MATLAB (MATLAB 2012b)). 2.4% of the strains for which

Gamma fitting could explain less than 80% of the variance of cells distribution across

the bins were filtered out (Fig. S13B) and the Gamma distribution was used to compute

the mean and variance for the rest. Finally, 5.8% of the cells for which the two replicates

gave substantially different results (the 2.5% and 5% of smallest/largest ratio of the two

replicates mean and noise values correspondingly of unfiltered data) were filtered out to

get the final accurate results for ~65% of the designed library strains.

Linear model of expression mean and noise with elastic-net regularization

The sets of promoters were used to learn a regularized linear regression model from

sequence features which predicts the value of mean expression, noise (CV2), and noise

strength (Fano factor). Learning was done using a 5-fold cross-validation scheme,

whereby model parameter fitting was done only on training data and the model was

evaluated on the held-out test data. The model was regularized using elastic-net (Zou

and Hastie 2005), where the value of lambda (the penalty coefficient) was learned using

a 5-fold internal cross-validation scheme on the training data (i.e. internally partitioning

the training data to learning and validation sets) and selecting the value that gave best




16

results on the validation set. The training R2 was calculated as the average R2 achieved

using internal cross-validation on the training set.

Kinetic model of gene expression

Gene expression is a function of TF binding to the promoter. Therefore, the way in

which TFs find their target has implications for gene expression output. A recent

study(Hammar et al. 2012) presented two observations regarding TF search. First, it

showed that the proximity of two TFBSs affects the time that it takes the TF to bind

them (Kon) in a manner that depends of the distance between the sites. Second, the

study showed that a DNA bound protein increases both the time between binding

events (Kon) and the bound TF dissociation (Koff) of a neighboring TFBS. These ideas

were used to integrate different mechanisms of TF search in a model of gene

expression.

Mean expression and expression noise for the set of all 27 combinations of 7 TF binding

sites in two sequence contexts (see Table S1) was predicted by mapping each

promoter configuration to a unique kinetic scheme in which the reactions represent

either binding or unbinding events at the promoter. A promoter that has N sites has 2N

possible promoter states (each site is either bound or not bound) for which the

transitions between them are defined by a transition matrix K, where Kij is the rate of

going from state j to state i. Only binding or unbinding events a single site at a time are

allowed; all other reaction rates are set to zero. Each promoter state has a transcription

rate defined in vector r, where ri is the transcription rate of state i. This system was

solved analytically by following the procedure described by Sanchez et al.(Sanchez et al.

2011) and assuming translation to happen instantaneously, i.e., that the mRNA half-life

is much shorter than the protein half-life, so that it can assumed that the number of

proteins produced per mRNA follows a geometric distribution with mean (burst size) b.

Protein degradation happens with rate delta, but is mostly a result of dilution from cell

division due to the high stability of the fluorescent reporter. The described kinetic

scheme is solved analytically using the Master equation to obtain the mean protein

abundance and noise. Alternatively, the kinetic scheme was solved numerically using




17

stochastic simulations (Gillespie algorithm(Gillespie 1977)). We note that both methods

gave similar results (R2=0.99, see Fig.S14).

Although the free parameter values of the model can be constrained to a biologically

meaningful regime (see Supplementary Material), the values of the free parameters

were learned from our measured data. In order to prevent overfitting, a 10-fold cross-

validation scheme was used in which the model performance was tested on a held out

subset of the data that was not used for learning.

For each of the two alternative models a different mapping between the free parameters

of the model and the transition matrix K was specified. The 3D diffusion, specific-binding

only model assumes that binding happens only at the specific site. All rates in this

model are independent of neighboring sites or bound TFs. The non-specific binding and

1D diffusion model assumes a general non-specific binding and unbinding rate and

unique binding and unbinding rates for each of the 7 binding sites. Therefore, the

effective rates of binding and unbinding were computed using the equations presented

by Hammar et al.(Hammar et al. 2012) in which a 1D diffusion coefficient, the non-

specific binding or unbinding rate, and the distance to the neighboring site determine

the effective rate of binding or unbinding, respectively. A computation of this rate

involves two scenarios: (1) the neighboring site is empty, in which case it is assumed

that it ‘steals’ effective binding from the current site; and (2) the neighboring site is

bound, in which case it acts as a ‘roadblock’ and decreases the effective rate of both

binding and unbinding. See Supplementary Material for the equations used.

Measurement of native S. cerevisiae promoter reporter library

Genomically integrated native promoter reporter strains from Keren at. el.(Keren et al.

2013) and isolated strains from the library were measured using fluorescence-activated

cell sorting (FACS) in SC-Glu-URA (synthetic complete media with 2% glucose and

without uracil) medium without amino acids, except for Histidine. For each strain a

minimum of 20,000 cells were collected.




18

Data Access Raw and processed data from this study have been submitted to the NCBI Gene Expression Omnibus (GEO; http://www.ncbi.nlm.nih.gov/geo/) under accession number GSE55346. Code used for the library construction and analysis is available in Supplemental Material and at http://genie.weizmann.ac.il/software/p_noise.html. Acknowledgments

This work was supported by grants from the European Research Council and the US

National Institutes of Health to E. Segal. E. Segal is the incumbent of the Soretta and

Henry Shapiro career development chair. We thank Shai Lubliner for help with

computational analyses.

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23

Figures

Fig. 1:

Fig. 1. Measuring the single cell gene expression distribution of thousands of designed promoter sequences within a single experiment. (A) Cells of the pooled

library of 6500 strains are sorted into 32 expression bins. (B) The single-cell expression

distribution of each strain is reconstructed by determining the fraction of cells that

contain each promoter in every expression bin using parallel sequencing of the

promoter region. Shown are single-cell expression distributions of 6 strains from the

library. The mean, noise and noise strength of each strain are then extracted from these

distributions (see Methods). (C) Shown is the mean expression (x-axis) and noise (y-

axis) of each of the 6500 different library strains. Colored points correspond to the six

strains shown in (B). Also shown is a vertical line corresponding to a nearly two orders

of magnitude range in noise.

Figure 1

Exp

ress

ion

nois

e

(log

scal

e, C

V2 )

10−1 100 101

10−2

10−1

100

Sorting by YFP/mCherry

32

Expression bins

Log2(YFP/mCherry)

Cel

ls (%

)

36.7 0.03 0

1.4

Expression bins

C A B

Expression mean (A.U., log scale)

10-2

10-1

100

100 10-1 101

Strain #3580

1 32

40

0

Cel

ls (%

)

Expression bins Strain #4926

1 32

20(

0(

Cel

ls (%

)

Strain #2633

1 32

10(

0(

Cel

ls (%

)

Expression bins

Strain #5167

1 32

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0

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ls (%

)

Expression bins Strain #4616

1 32

30

0

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ls (%

)

Strain #4489

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0

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ls (%

) Expression bins

16 16

16 16

16 16

Expression bins Expression bins Strain #3580 Strain #4926 Strain #2633 Strain #5167 Strain #4616 Strain #4489

1 2 3




24

Fig. 2:




25

Fig. 2. The effect of nucleosome disfavoring sequences and number of binding sites on noise. (A) Mean expression and noise of 182 promoters with 0 (blue points), 1

(light blue points), or 2 (red points) poly(dT:dA) of length 15bp and a single Gcn4 site.

Note that promoters with more poly(dT:dA) tend to have higher expression and lower

noise. (B) Shown is a comparison of the effect on expression noise of increasing the

mean expression either by adding a TF binding site or by adding a nucleosome

disfavoring sequence. Shown are 417 promoter pairs in which adding a TF binding site

or a poly(dT:dA) tract resulted in similar increase of the mean expression (all promoters

were divided into 50 bins according to their log expression values, promoters that share

a bin are considered to have similar expression levels). In 309 (74%) of these 417

promoter pairs, adding a TF site resulted in noisier expression as compared to adding a

nucleosome disfavoring sequence (binomial test P<10-22). (C) Mean expression and

noise of 643 promoters with 0 (dark blue points) to 7 (dark red points) binding sites of

Gcn4 and no other TF. The black arrows (A,B) point in the direction of expression and

noise change. Note the general increase in both expression mean and noise that results

with the addition of Gcn4 binding sites.




26

Fig. 3:

Fig. 3. A linear model based on promoter sequence features predicts a large fraction of the mean-independent component of the noise. (A,B,D,E) Shown is a

comparison of the predicted (x-axis) and measured (y-axis) noise for a model that

predicts noise using only mean expression (A,D) and for a model that also incorporates

promoter sequence features (B,E). Results are shown for promoters with a single Gcn4

site (A,B) or multiple sites (D,E). The noise of each promoter was predicted using a

model that was trained on the four subsets that did not include the promoter, out of 5

equally sized subsets to which we split the data. Pearson’s R-squared value (R2) and

Spearman’s rank correlation coefficient (ρ) are shown in each model plot (A,B,D,E).

(C,F) The weights of the sequence features used in the linear models presented in

(B,E) (the weight of the expression mean is not shown). The weights correspond to the

absolute value of the relative contribution of each feature to the prediction of the noise

component that is independent of the mean.

10−3 10−2 10−110−3

10−2

10−1

ultiple site, no cv, expression only, Rsq = 0.33482, Spearman = 0.6

Expression noise (CV2, log, predicted)

Expr

essi

on n

oise

(CV2 , l

og, m

easu

red)

R2=0.33 ρ=0.68

10−3 10−2 10−110−3

10−2

10−1

e site, no cv, expression and features, Rsq = 0.77927, Spearman =


Expr

essi

on n

oise

(CV2 , l

og, m

easu

red)

R2=0.77 ρ=0.88

mean_nuc_cov_sitenuc occ TrN adjacentN sites0

0.1

0.2

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Wei

ghts

Noise2 from only Features, R2=0.34225

N sitesexpressionN adjacentnuc occ Trmean_nuc_cov_site0

0.2

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1

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ghts

Noise2 from both Features and Exp, R2=0.59727

N sitesN adjacentmean_nuc_cov_sitenuc occ Tr0

0.05

0.1

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Wei

ghts

Exp from Features, R2=0.7342


0.05

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0.35

Wei

ghts

Noise resid. from Features, R2=0.7342

repr_anynuc_cov_sitenuc_cov_Trstrong_sitesite_pospT_lennegative_site0

0.1

0.2

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0.5

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ghts


expressionstrong_sitenuc_cov_sitesite_pospT_lenrepr_anynegative_sitenuc_cov_Tr0

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repr_anystrong_sitenuc_cov_TrpT_lensite_posnuc_cov_sitenegative_site0

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strong_sitenuc_cov_sitesite_pospT_lenrepr_anynegative_sitenuc_cov_Tr0

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ghts


Figure 3

A linear model can predict 63% (a) or 33% (e) respectively, for a set of promoters with a single binding site or a set with multiple binding sites, of the CV2 from expression level alone. When promoter features are taken into account, we can predict 81% (b) and 67% (f) respectively. Alternatively, we can predict the Fano factor, which does not correlate with mean expression, and explain 50% (c) and 52% (g) for the single and multiple site sets respectively. Since CV2 is expression dependent and Fano factor is not, we quantify for each promoter feature how well it can explain either mean expression (d,h red) or the Fano factor (d,h blue).

number of sites

mean nuc. cov. site

nuc. cov. TATA

number of adjacent sites

site affinity

nuc. cov. site

site position

polyT length

repressor activity

site orientation

nuc. cov. TATA

10−1 100 101 10210−4

10−3

10−2

10−1

100Expression vs. CV2

Mean Expression

CV2

10−1 100

10−3

10−2

10−1

Only Expression, R2=0.33482

Predicted CV2

CV2

10−4 10−2 100 10210−4

10−3

10−2

10−1

100Only Features, R2=0.68423

Predicted CV2

CV2

Multiple_Site − CV2

10−2 100 10210−4

10−3

10−2

10−1

100Both Features and Exp, R2=0.76599

Predicted CV2

CV2

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10−3

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10−1


Mean Expression

CV2

10−1 100

10−3

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Predicted CV2

CV2

10−4 10−2 100 10210−4

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CV2


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CV2

10−1

100

101

102

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Expression vs. CV2

Mean Expression

CV

2

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101

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10−1


Predicted CV2

CV

2

10−2

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102

104

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Only Features, R2=0.81906

Predicted CV2

CV

2

Single_Site − CV2

10−2

100

102

10−4

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100

Both Features and Exp, R2=0.82022

Predicted CV2

CV

2

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101

102

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Expression vs. CV2

Mean Expression

CV

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Predicted CV2

CV

2

10−3 10−2 10−1

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ingle site, no cv, expression only, Rsq = 0.6254, Spearman = 0.74


Expr

essi

on n

oise

(CV2 , l

og, m

easu

red)

R2=0.63 ρ=0.74

10−3 10−2 10−1

10−3

10−2

10−1

site, no cv, expression and features, Rsq = 0.82022, Spearman =


Expr

essi

on n

oise

(CV2 , l

og, m

easu

red)

R2=0.82 ρ=0.89

mean_nuc_cov_sitenuc occ TrN adjacentN sites0

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expressionstrong_sitenuc_cov_sitesite_pospT_lenrepr_anynegative_sitenuc_cov_Tr0

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Wei

ghts


repr_anystrong_sitenuc_cov_TrpT_lensite_posnuc_cov_sitenegative_site0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Wei

ghts


strong_sitenuc_cov_sitesite_pospT_lenrepr_anynegative_sitenuc_cov_Tr0

0.05

0.1

0.15

0.2

0.25

Wei

ghts


Figure 3

A linear model can predict 63% (a) or 33% (e) respectively, for a set of promoters with a single binding site or a set with multiple binding sites, of the CV2 from expression level alone. When promoter features are taken into account, we can predict 81% (b) and 67% (f) respectively. Alternatively, we can predict the Fano factor, which does not correlate with mean expression, and explain 50% (c) and 52% (g) for the single and multiple site sets respectively. Since CV2 is expression dependent and Fano factor is not, we quantify for each promoter feature how well it can explain either mean expression (d,h red) or the Fano factor (d,h blue).

number of sites

mean nuc. cov. site

nuc. cov. TATA

number of adjacent sites

site affinity

nuc. cov. site

site position

polyT length

repressor activity

site orientation

nuc. cov. TATA

10−1 100 101 10210−4

10−3

10−2

10−1


Mean Expression

CV2

10−1 100

10−3

10−2

10−1


Predicted CV2

CV2

10−4 10−2 100 10210−4

10−3

10−2

10−1


Predicted CV2

CV2


10−2 100 10210−4

10−3

10−2

10−1


Predicted CV2

CV2

10−1 100 101 10210−4

10−3

10−2

10−1


Mean Expression

CV2

10−1 100

10−3

10−2

10−1


Predicted CV2

CV2

10−4 10−2 100 10210−4

10−3

10−2

10−1


Predicted CV2

CV2


10−2 100 10210−4

10−3

10−2

10−1


Predicted CV2

CV2

10−1

100

101

102

10−4

10−3

10−2

10−1

100

Expression vs. CV2

Mean Expression

CV

2

10−1

100

101

10−4

10−3

10−2

10−1


Predicted CV2

CV

2

10−2

100

102

104

10−4

10−3

10−2

10−1

100


Predicted CV2

CV

2

Single_Site − CV2

10−2

100

102

10−4

10−3

10−2

10−1

100


Predicted CV2

CV

2

10−1

100

101

102

10−4

10−3

10−2

10−1

100

Expression vs. CV2

Mean Expression

CV

2

10−1

100

101

10−4

10−3

10−2

10−1


Predicted CV2

CV

2

10−2

100

102

104

10−4

10−3

10−2

10−1

100


Predicted CV2

CV

2

Single_Site − CV2

10−2

100

102

10−4

10−3

10−2

10−1

100


Predicted CV2

CV

2

Mod

el fe

atur

e w

eigh

t (ab

s. v

alue

)

A B

D E F

Predicting noise from expression

Predicting noise from expression!and sequence features

Noi

se (l

og, σ

2 /µ2 ,

mea

sure

d)

Noi

se (l

og, σ

2 /µ2 ,

mea

sure

d)

Noi

se (l

og, σ

2 /µ2 ,

mea

sure

d)

Noi

se (l

og, σ

2 /µ2 ,

mea

sure

d)

Noise (log, σ2/µ2, predicted)



Noise (log, σ2/µ2, predicted)M

odel

feat

ure

wei

ghts

(abs

. val

ue)C

Mod

el fe

atur

e w

eigh

ts (a

bs. v

alue

)




27

Fig. 4:

Fig. 4. The effect of multiple transcription factor binding sites on noise is largely mediated by 1D sliding of the cognate transcription factor. For each promoter with

a different number and configuration of seven possible TFBS (A, top) we constructed a

kinetic model. Each of the 127 possible configurations was represented by a unique

kinetic scheme and transition matrix (A, middle). The rate parameters of the reactions in

the matrix were computed from the free parameters of the model using one of two

alternative mappings that assume either that TFs search for their target through 3D

diffusion (B, left) or that they do so by a combination of 3D and 1D diffusion (B, right).

The transition matrix, together with reactions for transcription, translation and mRNA

and protein degradation, were simulated and solved analytically to obtain the steady

state mean protein abundance and noise (A, bottom). (C) The free parameters of the

models were fitted in a leave-one-out cross-validation and the predictions (x-axis) of

mean expression and CV2 were compared to the measured (y-axis) (see Fig. S12 for a

10-fold cross-validation). The results show that the model that incorporates both 3D and

1D diffusion performs significantly better for both mean expression and noise than the

model that assumes only 3D diffusion.

10−3 10−2 10−1

10−3

10−2

10−1

Noise (log, m2/µ2, measured)

Noi

se (l

og, m

2 /µ2 , p

redi

cted

)

100 101

100

101

Mean (log, µ, measured)

Mea

n (lo

g, µ

, pre

dict

ed)

10−3 10−2 10−1

10−3

10−2

10−1

Noise (log, m2/µ2, measured)

Noi

se (l

og, m

2 /µ2 , p

redi

cted

)

100 101

100

101

Mean (log, µ, measured)

Mea

n (lo

g, µ

, pre

dict

ed)

Spec

ific

bind

ing

Non

-spe

cific

bin

ding"

and

1D s

lidin

g

Mean expression Expression noise

12

127

34567

Gcn4 binding site

Mean expression

Exp

ress

ion

nois

e

4

1mRNA protein

∅ ∅

Kn

1

4

−!" !"!" −!"

!

!!! =

−!"# !"##!"# −!"## !

!!

!! =−!"#! !"##! !"#! !"#!!"#! !"#! !"#! !"#!0 !"#! !"#! !"#!

!"#! !"#! !"#! !"#!!

A BSet of 128 promoter configurations:

Each configuration maps to a unique kinetic scheme and transition matrix:

Each kinetic scheme is solved analytically to get the mean and noise of the expression distribution:

C

specific binding non-specific binding and 1D sliding

Kon

Koff

Kon1

Koff1

Kon1

Koff1

Kon

2

Koff2

Kon

2

Koff2

−!" !"!" −!"

!

!!! =

−!"# !"##!"# −!"## !

!!

!! =!!

−!"#!−!"#! !"##! !"!!! 0!"#! −!"##! − !"#! 0 !"!!!!"#! 0 −!"!!! − !"#! !"##!0 !"#! !"#! −!"##! − !"##!

!

−!" !"!" −!"

!

!!! =

−!"# !"##!"# −!"## !

!!

!! =!!

−!"#!−!"#! !"##! !"!!! 0!"#! −!"##! − !"#! 0 !"!!!!"#! 0 −!"!!! − !"#! !"##!0 !"#! !"#! −!"##! − !"##!

!

R2=0.68ρ=0.83

R2=0.81 ρ=0.86

R2=0.22ρ=0.58

R2=0.53 ρ=0.78

Mean (log, µ, measured) Noise (log, σ2/µ2, measured)

Mean (log, µ, measured) Noise (log, σ2/µ2, measured)

Mea

n (lo

g, µ

, pre

dict

ed)

Mea

n (lo

g, µ

, pre

dict

ed)

Noi

se (l

og, σ

2 /µ2 ,

pred

icte

d)N

oise

(log

, σ2 /µ

2 , pr

edic

ted)

−!" !"!" −!"

!

!!! =

−!"# !"##!"# −!"## !

!!

!! =!!

−!"#!−!"#! !"##! !"!!! 0!"#! −!"##! − !"#! 0 !"!!!!"#! 0 −!"!!! − !"#! !"##!0 !"#! !"#! −!"##! − !"##!

!

−!" !"!" −!"

!

!!! =

−!"# !"##!"# −!"## !

!!

!! =!!

−!"#!−!"#! !"##! !"!!! 0!"#! −!"##! − !"#! 0 !"!!!!"#! 0 −!"!!! − !"#! !"##!0 !"#! !"#! −!"##! − !"##!

!…




Probing the effect of promoters on noise in gene …1" Title: Probing the effect of promoters on...

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